1 |
A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis 14 (1973), 349-381. https://doi.org/10.1016/0022-1236(73)90051-7
DOI
|
2 |
G. Autuori and P. Pucci, Elliptic problems involving the fractional Laplacian in , J. Differential Equations 255 (2013), no. 8, 2340-2362. https://doi.org/10.1016/j.jde.2013.06.016
DOI
|
3 |
T. Bartsch and Z. Q. Wang, Existence and multiplicity results for some superlinear elliptic problems on , Comm. Partial Differential Equations 20 (1995), no. 9-10, 1725-1741. https://doi.org/10.1080/03605309508821149
DOI
|
4 |
L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007), no. 7-9, 1245-1260. https://doi.org/10.1080/03605300600987306
DOI
|
5 |
G. M. Bisci and V. D. Radulescu, Ground state solutions of scalar field fractional Schrodinger equations, Calc. Var. Partial Differential Equations 54 (2015), no. 3, 2985-3008. https://doi.org/10.1007/s00526-015-0891-5
DOI
|
6 |
C. Brandle, E. Colorado, A. de Pablo, and U. Sanchez, A concave-convex elliptic problem involving the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A 143 (2013), no. 1, 39-71. https://doi.org/10.1017/S0308210511000175
DOI
|
7 |
H. Brezis, Analyse fonctionnelle, Collection Mathematiques Appliquees pour la Maitrise., Masson, Paris, 1983.
|
8 |
X. Chang, Ground state solutions of asymptotically linear fractional Schrodinger equations, J. Math. Phys. 54 (2013), no. 6, 061504, 10 pp. https://doi.org/10.1063/1.4809933
DOI
|
9 |
X. Chang and Z.-Q. Wang, Nodal and multiple solutions of nonlinear problems involving the fractional Laplacian, J. Differential Equations 256 (2014), no. 8, 2965-2992. https://doi.org/10.1016/j.jde.2014.01.027
DOI
|
10 |
M. Cheng, Bound state for the fractional Schrodinger equation with unbounded potential, J. Math. Phys. 53 (2012), no. 4, 043507, 7 pp. https://doi.org/10.1063/1.3701574
DOI
|
11 |
N. Laskin, Fractional quantum mechanics and Levy path integrals, Phys. Lett. A 268 (2000), no. 4-6, 298-305. https://doi.org/10.1016/S0375-9601(00)00201-2
DOI
|
12 |
S. Dipierro, G. Palatucci, and E. Valdinoci, Existence and symmetry results for a Schrodinger type problem involving the fractional Laplacian, Matematiche (Catania) 68 (2013), no. 1, 201-216. https://doi.org/10.4418/2013.68.1.15
|
13 |
E. Di Nezza, G. Palatucci, and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math. 136 (2012), no. 5, 521-573. https://doi.org/10.1016/j.bulsci.2011.12.004
DOI
|
14 |
P. Felmer, A. Quaas, and J. Tan, Positive solutions of the nonlinear Schrodinger equation with the fractional Laplacian, Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 6, 1237-1262. https://doi.org/10.1017/S0308210511000746
DOI
|
15 |
H. Jin and W. Liu, Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth, Electron. J. Differential Equations 2017 (2017), Paper No. 80, 19 pp.
|
16 |
J. Korvenpaa, T. Kuusi, and G. Palatucci, Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations, Math. Ann. 369 (2017), no. 3-4, 1443-1489. https://doi.org/10.1007/s00208-016-1495-x
DOI
|
17 |
N. Laskin, Fractional Schrodinger equation, Phys. Rev. E (3) 66 (2002), no. 5, 056108, 7 pp. https://doi.org/10.1103/PhysRevE.66.056108
DOI
|
18 |
N. Laskin, Fractional quantum mechanics, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2018. https://doi.org/10.1142/10541
|
19 |
S. Secchi, Perturbation results for some nonlinear equations involving fractional operators, Differ. Equ. Appl. 5 (2013), no. 2, 221-236. https://doi.org/10.7153/dea-05-14
|
20 |
S. Secchi, Ground state solutions for nonlinear fractional Schrodinger equations in , J. Math. Phys. 54 (2013), no. 3, 031501, 17 pp. https://doi.org/10.1063/1.4793990
DOI
|
21 |
M. M. Fall, F. Mahmoudi, and E. Valdinoci, Ground states and concentration phenomena for the fractional Schrodinger equation, Nonlinearity 28 (2015), no. 6, 1937-1961. https://doi.org/10.1088/0951-7715/28/6/1937
DOI
|
22 |
S. Secchi, On fractional Schrodinger equations in without the Ambrosetti-Rabinowitz condition, Topol. Methods Nonlinear Anal. 47 (2016), no. 1, 19-41.
|
23 |
K. Teng, Multiple solutions for a class of fractional Schrodinger equations in RN, Nonlinear Anal. Real World Appl. 21 (2015), 76-86. https://doi.org/10.1016/j.nonrwa.2014.06.008
DOI
|
24 |
R. Servadei and E. Valdinoci, Variational methods for non-local operators of elliptic type, Discrete Contin. Dyn. Syst. 33 (2013), no. 5, 2105-2137. https://doi.org/10.3934/dcds.2013.33.2105
DOI
|
25 |
J. Tan, The Brezis-Nirenberg type problem involving the square root of the Laplacian, Calc. Var. Partial Differential Equations 42 (2011), no. 1-2, 21-41. https://doi.org/10.1007/s00526-010-0378-3
DOI
|
26 |
J. Tan, Y. Wang, and J. Yang, Nonlinear fractional field equations, Nonlinear Anal. 75 (2012), no. 4, 2098-2110. https://doi.org/10.1016/j.na.2011.10.010
DOI
|
27 |
H. Zhang, J. Xu, and F. Zhang, Existence and multiplicity of solutions for superlinear fractional Schrodinger equations in RN, J. Math. Phys. 56 (2015), no. 9, 091502, 13 pp. https://doi.org/10.1063/1.4929660
DOI
|
28 |
W. Zhang, X. Tang, and J. Zhang, Infinitely many radial and non-radial solutions for a fractional Schrodinger equation, Comput. Math. Appl. 71 (2016), no. 3, 737-747. https://doi.org/10.1016/j.camwa.2015.12.036
DOI
|